Faraday rotation, or the Faraday effect, is an interaction between light and a magnetic field. When linearly polarized light passes through a parallel magnetic field, the plane of the linearly polarized light is rotated. The rotation of the plane of polarization is proportional to the intensity component of the magnetic field in the direction of the beam of light. Light that is reflected back through the magnetic field is further rotated in the same direction.
The empirical angle of rotation is given byβ=VBd,where β is the angle of rotation (in radians), V is the Verdet constant for the material, B is the magnetic flux density in the direction of propagation (in teslas), and d is the length of the path (in meters).
The Verdet constant reflects the strength of the Faraday effect for a particular material. The Verdet constant can be positive or negative, with a positive Verdet constant corresponding to a counterclockwise rotation when the direction of propagation is parallel to the magnetic field. The Verdet constant for most materials is extremely small and is wavelength dependent. Typically, the longer the wavelength the smaller the Verdet constant.
As can be seen from the relationship between the Verdet constant, the path length, and the angle of rotation, a desired angle of rotation can be achieved in a shorter distance where the Verdet constant is high. The highest Verdet constants are found in terbium gallium garnet (TGG), which has a Verdet constant of −40 rad/T·m at 1064 nm.